Indulal Spectra of two new joins of graphs and infinite families of integral graphs Kragujevac J. Liu J. Zhou and C. Liu Z.

## CiteSeerX — The Laplacian spectrum of graphs

Zhang Spectra of subdivision-vertex and subdivision-edge joins of graphs in: Bull. Sanming Zhou Ed s Springer McLeman and E. Vandam and W. Haemers Which graphs are determined by their spectrum? Linear Algebra Appl.

Home About us Subjects Contacts. Advanced Search Help. Entire Site De Gruyter Online. Sign in Register. English Deutsch. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested.

Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.

Graphs determined by signless Laplacian spectra. In the past decades, graphs that are determined by their spectrum have received more attention, since they have been applied to several fields, such as randomized algorithms, combinatorial optimization problems and machine learning. An important part of spectral graph theory is devoted to determining whether given graphs or classes of graphs are determined by their spectra or not.

So, finding and introducing any class of graphs which are determined by their spectra can be an interesting and important problem.

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A graph is said to be D Q S if there is no other non-isomorphic graph with the same signless Laplacian spectrum. Applying these results, some D Q S graphs with independent edges and isolated vertices are obtained. Applying these results, some DQS graphs with independent edges are Applying these results, some DQS graphs with independent edges are obtained. Combinatorial approach for computing the characteristic polynomial of a matrix. Graphs whose signless Laplacian spectral radius does not exceed the Hoffman limit value.

Switching is an equivalence relation partitioning the graphs on n vertices into switching classes. The rich properties of a nutful NSSD reveal new spectral properties of conference graphs. Luke Collins.

Finding and discovering any class of graphs which are determined by their spectra is always an important and interesting problem in the spectral graph theory. The main aim of this study is to characterize two classes of multicone graphs The main aim of this study is to characterize two classes of multicone graphs which are determined by both their adjacency and Laplacian spectra.

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A multicone graph is defined to be the join of a clique and a regular graph. Let Kw denote a complete graph on w vertices, and let m be a positive integer number. Maximum number of review items at one time. Mathematical Reviews Reviewer Information. Bioinformatics methods based on sequence alignment may fail when there is a low amino acidic identity percentage between query sequence.

### Table of contents

Spectral characterization of new classes of multicone graphs. This paper deals with graphs that are known as multicone graphs. A multicone graph is a graph obtained from the join of a clique and a regular graph. Let w, l, m be natural numbers and k is a natural number.

It is proved that any Also, we show that complements of some of these mul-ticone graphs are determined by their adjacency spectra. Moreover, we prove that any connected graph cospectral with these multicone graphs must be perfect. Finally , we pose two problems for further researches. Mathematics Subject Classification : 05C Haemers [15] conjectured that almost all graphs are determined by their spectra.

## Visualizing graph spectra like chemical spectra

Nevertheless, the set of graphs which are known to be determined by their spectra is small. Hence, discovering infinite classes of Hence, discovering infinite classes of graphs that are determined by their spectra can be an interesting problem. The aim of this paper is to characterize new classes of multicone graphs that are determined by their spectrum. It is proved that any graph cospectral with multicone graph Kw L P is determined by its adjacency spectrum as well as its Laplacian spectrum, where Kw and L P denote a complete graph on w vertices and the line graph of the Petersen graph, respectively.

Finally, three problems for further researches are proposed.

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